Calculating a Fix for the HP-41

This program is supplied without representation or warranty of any kind.
Jean-Marc Baillard and The Museum of HP Calculators therefore assume no
responsibility and shall have no liability, consequential or otherwise, of
any kind arising from the use of this program material or any part thereof.

Overview

-After measuring the altitudes of n = 2 , 3 ( or more ) stars,
the 2 following programs compute your geographical position:
Longitude & Latitude
-The second routine is longer but faster than the first one.

-Longitudes are reckoned positively Eastwards from the meridian of Greenwich.

-If the process seems to diverge, stop the program, GTO "FIX" ,
XEQ 03 and key in new estimated step/longitude/latitude.
-Too bad initial guesses may lead to a relative minimum and a wrong
position but in this case, Z-output is not very small.
-However, if n = 2, the system has 2 solutions. Therefore, measuring
3 altitudes is safer.

-Longitudes are reckoned positively Eastwards from the meridian of Greenwich.

-If the process seems to diverge, stop the program, GTO "FIX2" ,
XEQ 03 and key in new estimated longitudes/latitudes.
-Too bad initial guesses may lead to a relative minimum and a wrong
position but in this case, Z-output is not very small.
-However, if n = 2, the system has 2 solutions. Therefore 3 measured
altitudes are safer.
-"SXY" may also stop prematurely if the jacobian = 0 ( always check
Z-register or R19 )
-"SXY" tries to produce very accurate results, but here, 8 decimals
are superfluous.
So, execution time can be reduced if you modify the final test
in the "SXY" listing.